EX-2

When an individual becomes ill, their demand for health services is $q = 20 - p$, where $p$ is the price per unit of service. The market price of a medical unit is 8 ₪. The probability of becoming sick is 0.5.

An insurance company offers a policy with a premium of 56 ₪, under which the individual may consume up to 14 units of medical services for free.

Evaluate: "If the individual is risk-averse and the insurance premium is actuarially fair, then the individual will certainly purchase the insurance."

Evaluate: "A risk-averse individual will prefer a certain lottery to a risky lottery even if the expected prize of the certain lottery is lower."

Evaluate: "Insurance with a deductible may reduce the moral hazard problem but worsen the adverse selection problem."

Three illness states, each with probability $1/3$. Mild: $Q = 80 - 2P$, $MC = 20$ ₪. Moderate: $Q = 100 - P$, $MC = 30$ ₪. Severe: $Q = 200$ (perfectly inelastic), $MC = 50$ ₪. Market price equals MC in each state.

What is the individual's expected expenditure on medical services if they are not insured?

What is the actuarially fair premium for full insurance?

In which illness states might moral hazard arise if full insurance is provided?

If the individual is risk-averse, would they necessarily purchase full insurance at the actuarially fair price?

Suppose the insurance company introduces 10% coinsurance (the individual pays 10% of the price of each unit). What is the actuarially fair premium in this case?

The insurer offers two plans — Plan A: Full insurance at the actuarially fair premium. Plan B: Full insurance only in the severe illness state. Would a risk-averse individual prefer Plan B to Plan A? Could the individual prefer no insurance at all?

Progressive's "Autograph" automobile insurance installs a device that transmits distance driven, locations, and time of driving. A Houston pilot found Autograph adopters saved 25% on premiums vs traditional insurance.

Can this result be explained by moral hazard? By adverse selection?

If Progressive offers Autograph nationwide while maintaining traditional insurance, how will the traditional insurance premium and the share of drivers in the traditional system evolve over time?